1. Stellar Properties from Red Giants to White Dwarfs

2. Topics Distances The Solar Neighborhood
Naming the Stars
Luminosity and Apparent Brightness
More on the Magnitude Scale
Stellar Temperatures
Stellar Sizes
Estimating Stellar Radii
The Hertzsprung–Russell Diagram
The Hipparcos Mission

3. Topics, cont. Extending the Cosmic Distance Scale Stellar Masses
Mass and Other Stellar Properties

4. Measuring Distances to the Stars
Which of these stars is
closest to the Sun?
the brightest?
Which of these stars has
the largest diameter?
the lowest temperature?

5. Measuring Distances to the Stars
A light year is the distance light travels in one year.
c = 186,000 mi/s or
300,000 km/s
1ly = 6 trillion miles
1ly = 10 trillion km
A light year cannot be measured directly. It is derived, based on measurements of the speed light.

6. Measuring Distances to the Stars
Stellar distances can be measured using parallax:
January
July

7. Measuring Distances to the Stars
THE PARSEC
One parsec is the distance of a star that has a parallax angle of one arc second.
D = 1/p,
where
D = distance in parsec
p = parallax in arcseconds

8. The Solar Neighborhood
Nearest star to the Sun: Proxima Centauri
which is a member of a 3-star system: Alpha Centauri complex
Model of distances:
Sun is a marble, Earth is a grain of sand orbiting 1 m away
Nearest star is another marble 270 km away
Solar system extends about 50 m from Sun; rest of distance to nearest star is basically empty

9. The Solar Neighborhood
Next nearest neighbor: Barnard’s Star
Barnard’s Star has the largest proper motion of any – proper motion is the actual shift of the star in the sky, after correcting for parallax.
These pictures were taken 22 years apart:

10. The Solar Neighborhood
Actual motion of the Alpha Centauri complex:

11. The Solar Neighborhood
The 30 closest stars to the Sun:

12. The Solar Neighborhood
Naming stars:
Brightest stars were known to, and named by, the ancients (Procyon)
In 1604, stars within a constellation were ranked in order of brightness, and labeled with Greek letters (Alpha Centauri)
In the early 18th century, stars were numbered from west to east in a constellation (61 Cygni)

13. The Solar Neighborhood
As more and more stars were discovered, different naming schemes were developed (G51-15, Lacaille 8760, S 2398)
Now, new stars are simply labeled by their celestial coordinates
You cannot buy a star and have it named after someone. While these names are registered they are not recognized by the IAU.

14. Apparent Magnitude Hipparchus made 1st star catalog in 120 BC.
Divided stars into brightness categories.
1st mag brightest stars in the sky
5th mag faintest stars visible to unaided eye.

15. Magnitude Scale m=-2.5log(I) 2nd mag is 2.5x fainter than 1st mag.
3rd mag is 2.5x fainter than 2nd mag.
2.5x2.5x2.5x2.5x2.5~100
So a 5th mag star is about 100x fainter than a 1st mag star.

16. Apparent Magnitude Scale
Apparent luminosity is measured using a magnitude scale, which is related to our perception.
It is a logarithmic scale; a change of 5 in magnitude corresponds to a change of a factor of 100 in apparent brightness.
It is also inverted – larger magnitudes are dimmer.

17. Apparent Magnitude
Stellar brightness depends on the star’s actual brightness and on its distance.
Inverse Square Law
Double distance intensity drops by 22.
Triple distance intensity drops by 32.

18. Luminosity and Apparent Brightness
Therefore, two stars that appear equally bright might be a closer, dimmer star and a farther, brighter one:

19. Luminosity and Apparent Brightness
Luminosity, or absolute brightness, is a measure of the total power radiated by a star.
Apparent brightness is how bright a star appears when viewed from Earth; it depends on the absolute brightness but also on the distance of the star:

20. Luminosity and Apparent Brightness
If we know a star’s apparent magnitude and its distance from us, we can calculate its absolute (actual) luminosity.
Absolute magnitude is the brightness stars would appear to be if they were all place at a standard distance of 10 pc.
Therefore, absolute magnitude is an actual comparison of stellar luminosity, or brightness.

21. Stellar Temperatures
The color of a star is indicative of its temperature:
Red stars are relatively cool, while blue ones are hotter.
When I get in my car I turn the heater on to blue and the AC to red.

22. Anne Jump Cannon
Used objective prism plates to classify star spectra.
A, B …
A class had strongest H lines.
Later her classifications were reorganized by temperature from hottest to coolest.

23. Stellar Temperatures Stellar spectra are very informative.
There are seven general categories of stellar spectra, corresponding to different temperatures.
From highest to lowest, those categories are:
O B A F G K M

24. Stellar Temperatures
Here are their spectra:

25. Stellar Temperatures
Characteristics of the spectral classifications:

26. Stellar Sizes
A few very large, very close stars can be imaged directly using speckle interferometry; this is Betelgeuse:

27. Stellar Sizes
For the vast majority of stars that cannot be imaged directly, size must be calculated knowing the luminosity and temperature:
L a R2xT4
Giant stars have radii between 10 and 100 times the Sun’s.
Dwarf stars have radii equal to, or less than, the Sun’s.
Supergiant stars have radii more than 100 times the Sun’s.

28. Betelgeuse Spectral class = M2 Cool red star (3000K) Very bright star
It must be huge!
~ 1 au in radius
Distance modulus = m-M
m = +0.45
m-M = 0.45-(-5.1) = 5.55
It is 5.55 mag away.

29. The Hertzsprung–Russell Diagram
The H–R diagram plots stellar luminosity against surface temperature.
This is an H–R diagram of a few prominent stars:

30. The Hertzsprung–Russell Diagram
Once many stars are plotted on an H–R diagram, a pattern begins to form:
These are the 80 closest stars to us; note the dashed lines of constant radius.
The darkened curve is called the main sequence, as this is position where most stars are plotted.
Also indicated is the white dwarf region; these stars are hot but not very luminous, as they are quite small.

31. The Hertzsprung–Russell Diagram
An H–R diagram of the 100 brightest stars looks quite different:
These stars are all more luminous than the Sun. Two new categories appear here – the red giants and the blue giants.
Clearly, the brightest stars in the sky appear bright because of their enormous luminosities, not their proximity.

32. The Hertzsprung–Russell Diagram
This is an H–R plot of about 20,000 stars. The main sequence is clear, as is the red giant region.
About 90% of stars lie on the main sequence; 9% are red giants and 1% are white dwarfs.

33. Weighing the Stars Astronomers cannot bring a star into a
laboratory and place it on a scale.
So, how do astronomers determine the mass
of a star?

34. Visual Binaries Determination of stellar masses:
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.
Visual binaries can be measured directly; this is Kruger 60:

35. Spectroscopic Binaries
Spectroscopic binaries can be measured using their Doppler shifts:

36. Eclipsing Binaries
Finally, eclipsing binaries can be measured using the changes in luminosity:

37. Mass and Other Stellar Properties
Mass is the main determinant of where a star will be on the main sequence:

38. Mass and Other Stellar Properties
Mass is also correlated with radius, and very strongly correlated with luminosity:

39. Mass and Other Stellar Properties
Mass is also related to stellar lifetime:
Using the mass–luminosity relationship:

40. Mass and Other Stellar Properties
So the most massive stars have the shortest lifetimes – they have a lot of fuel but burn it at a very rapid pace.
On the other hand, small red dwarfs burn their fuel extremely slowly, and can have lifetimes of a trillion years or more.

41. Summary Can measure distances to nearby stars using parallax
Apparent magnitude is related to apparent brightness
Absolute magnitude is a measure of the power output of the star
Spectral analysis has led to the defining of seven spectral classes of stars
Stellar radii can be calculated if distance and luminosity are known

42. Summary, cont.
Besides “normal” stars, also have red giants, red supergiants, blue giants, blue supergiants, red dwarfs, and white dwarfs
Luminosity class can distinguish giant star from main-sequence one in the same spectral class
If spectrum is measured, can find luminosity; combining this with apparent brightness allows distance to be calculated

43. Summary, cont.
Measurements of binary-star systems allow stellar masses to be measured directly.
Mass is well correlated with radius and luminosity
Stellar lifetimes depend on mass; the more the mass, the shorter the lifetime